1、蘇州大學(xué)碩士學(xué)位論文實(shí)線性空間中Heing向量真有效性和它的標(biāo)量化姓名：范茜申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：丘京輝20090401HenigvectorialproperefficiencyinreallinearspaceAbstract●，1^●●●ltenigvectorialDroDeretticlencVinreallinearspaceanditsScalarizationsAbstractIntheframewo

2、rkofreallinearspaces，weintroducethreekindsofHenigproperefficientpointsByusingtheHahnBanachseparationtheoremonconvexsetsinreallinearspaces，weestablishthescalarizationtheoremsofthethreekindsofHcnigproperefficientpointsresp

3、ectivelyFromthis，weobtainthescalarizationsonHenigproperefficientsolutionsofvectoroptimizationproblemsinvolvingnearlyconesubconvexlikevector—valuedmapsandset—valuedmapsrespectivelyMoreover，byusingtheHahn—Banachseparationt

4、heoremonproductspaces，wegiveLagrangemultipliertheoremsOilHenigproperefficientsolutionsofvectoroptimizationproblemsinvolvingvector—valuedmapsandset—valuedsetmapswithconstraintManyknownresultshavebeenextendedtoreallinearsp

5、acesAnewconceptofHenigproperefficiencyonlyinvolvingrelativelyalgebricinterior，isintroducedanditsscalarizationisobtainedKeywords：reallinearspaces；Henigproperefficiency；scalarization；Lagrangemul—tipliertheoremIIWrittenbyFa